Generalized Stanley-Reisner rings and translative group actions

The Stanley-Reisner correspondence, which assigns a commutative ring to each finite simplicial complex, is a useful and well-studied bridge between commutative algebra and combinatorics. In 1987 Sergey Yuzvinsky proposed a construction that allows to see the Stanley-Reisner ring of a finite simplicial complex as the ring of global sections of a sheaf of rings on a poset. Motivated by applications in the theory of Abelian arrangements, Emanuele Delucchi and I extend Yuzvinsky's construction to the case of (possibly infinite) finite-length simplicial posets. This generalization behaves well with respect to quotients of simplicial complexes and posets by translative group actions.